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Fiberglass isn't kind to foam. The acetone in the resin usually eats foam, plus, it would make the cardboard soft and warp it.... You could try to make it entirely out of foam and seal the whole thing with a layer of bondo.

You could also seal it with with "podgy"? It is a thick white glue that dries clear. It is used for sealing in collages or those 3 D pictures that crafters like to make. I'm pretty sure you can paint acrylic paint over top of it.

styrospray you can get it from : http://www.industrialpolymers.com/
I have used it before, it will create a hard shell over your model, it will not eat foam, or cardboard, and is less toxic to work with then fiberglass, although pretty sticky stuff. I don't think it is not as strong as fiberglass (no fibers in it), although people use it for outdoor sculptures so it is pretty tuff.

you can spray or brush it on. It is self leveling so you get a pretty smooth surface. I had better luck after brushing it on the rotating the object to ensure a smooth, drip free surface. If you get drips, that is what sand paper is for.